A pulley device for a belt that includes an eccentric adjusting member fixed on a support, an eccentric hub rotatably mounted on the eccentric adjusting member, a torsion spring between the eccentric adjusting member and hub to exert a biasing force, and a pulley rotatably mounted on the hub. The hub provides an upper radial surface and the eccentric adjusting member provides a radially outwardly projecting flange formed at an upper end of the eccentric adjusting member and forming an axial abutment for the upper radial surface. The upper radial surface provides a pair of axially projected stops formed integrally within, each stop being dedicated to come into abutment against a corresponding stop provided by the radially outwardly projecting flange of the eccentric adjusting member. The hub further provides engaging means adapted to cooperate with an external tool, the engaging means circumferentially located between the projected stops of the hub.